Question

Exercitiile 2, 3 . Va rog frumos.

Answer 1

$2)a) {m}^{2} - 64 = (m - 8)(m + 8)$

$b)16 {x}^{2} - 81 {y}^{2} = (4x - 9y)(4x + 9y)$

$c)1 - {x}^{2} = (1 - x)(1 + x)$

$d) {x}^{2} - 49 {y}^{2} = (x - 7y)(x + 7y)$

$e) {x}^{2} - 13 = (x - \sqrt{13} )(x + \sqrt{13} )$

$f)10 - {y}^{2} = ( \sqrt{10} - y)( \sqrt{10} + y)$

$g)3 {x}^{2} - 1 = ( \sqrt{3} x - 1)( \sqrt{3} x + 1)$

$h) \frac{3}{4} {x}^{2} - 7 = ( \frac{ \sqrt{3} }{2} x - \sqrt{7} )( \frac{ \sqrt{3} }{2} x + \sqrt{7} )$

$i) \frac{16}{25} - {y}^{2} = ( \frac{4}{5} - y)( \frac{4}{5} + y)$

$j)9 {x}^{2} - 196 = (3x - 14)(3x + 14)$

$k) \frac{ {a}^{2} }{25} - \frac{16}{49} = ( \frac{a}{5} - \frac{4}{7} )( \frac{a}{5} + \frac{4}{7} )$

$l)4 {x}^{2} - 3 {y}^{2} = (2x - \sqrt{3} y)(2x + \sqrt{3} y)$

$m) {( \frac{2}{5}x) }^{2} - {( \frac{1}{7}) }^{2} = \frac{4}{25} {x}^{2} - \frac{1}{49} = ( \frac{2}{5} x - \frac{1}{7} )( \frac{2}{5} x + \frac{1}{7} )$

$n)3 {x}^{2} - 5 {y}^{2} = ( \sqrt{3} x - \sqrt{5} y)( \sqrt{3} x + \sqrt{5} y)$

$o)4 {a}^{2} - 3 = ( 2a - \sqrt{3} )(2a + \sqrt{3} )$

$p)2 {a}^{2} - 3 {b}^{2} = ( \sqrt{2} a - \sqrt{3} b)( \sqrt{2} a + \sqrt{3} b)$

$3)a) {x}^{2} - 121 = (x - 11)(x + 11)$

$b) {x}^{2} - 100 = (x - 10)(x + 10)$

$c)169 - {x}^{2} = (13 - x)(13 + x)$

$d)3 {x}^{2} - 1 = ( \sqrt{3} x - 1)( \sqrt{3} x + 1)$

$e)1 - 25 {a}^{2} {b}^{2} = (1 - 5ab)(1 + 5ab)$

$f)36 - 4 {a}^{2} {b}^{2} = (6 - 2ab)(6 + 2ab)$

Answer 2

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